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Computing & Information Sciences Kansas State University Monday, 03 Nov 2008CIS 560: Database System Concepts Measures of Query Cost: Review Cost is generally measured as total elapsed time for answering query Many factors contribute to time cost disk accesses, CPU, or even network communication Typically disk access is the predominant cost, and is also relatively easy to estimate. Measured by taking into account Number of seeks * average-seek-cost Number of blocks read * average-block-read-cost Number of blocks written * average-block-write-cost Cost to write a block is greater than cost to read a block data is read back after being written to ensure that the write was successful
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Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Lecture 27 of 42
Monday, 03 November 2008
William H. HsuDepartment of Computing and Information Sciences, KSU
KSOL course page: http://snipurl.com/va60Course web site: http://www.kddresearch.org/Courses/Fall-2008/CIS560
Instructor home page: http://www.cis.ksu.edu/~bhsu
Reading for Next Class:MySQL 5.1 documentation
Fast JoinsDiscussion: MP6, Other DB Operations
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Chapter 13: Query Processing
Overview Measures of Query Cost Selection Operation Sorting Join Operation Other Operations Evaluation of Expressions
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Measures of Query Cost:Review
Cost is generally measured as total elapsed time for answering query Many factors contribute to time cost
disk accesses, CPU, or even network communication Typically disk access is the predominant cost, and is also
relatively easy to estimate. Measured by taking into account Number of seeks * average-seek-cost Number of blocks read * average-block-read-cost Number of blocks written * average-block-write-cost
Cost to write a block is greater than cost to read a block data is read back after being written to ensure that the write was
successful
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Measures of Query Cost (Cont.) For simplicity we just use the number of block transfers from disk
and the number of seeks as the cost measures tT – time to transfer one block tS – time for one seek Cost for b block transfers plus S seeks
b * tT + S * tS We ignore CPU costs for simplicity
Real systems do take CPU cost into account We do not include cost to writing output to disk in our cost formulae Several algorithms can reduce disk IO by using extra buffer space
Amount of real memory available to buffer depends on other concurrent queries and OS processes, known only during executionWe often use worst case estimates, assuming only the minimum amount of
memory needed for the operation is available Required data may be buffer resident already, avoiding disk I/O
But hard to take into account for cost estimation
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
External Sort-Merge
1. Create sorted runs. Let i be 0 initially. Repeatedly do the following till the end of the relation: (a) Read M blocks of relation into memory (b) Sort the in-memory blocks (c) Write sorted data to run Ri; increment i.Let the final value of i be N
2. Merge the runs (next slide)…..
Let M denote memory size (in pages).
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Example: External Sorting Using Sort-Merge
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
External Merge Sort (Cont.)
Cost analysis: Total number of merge passes required: logM–1(br/M). Block transfers for initial run creation as well as in each pass
is 2br
for final pass, we don’t count write cost we ignore final write cost for all operations since the output of an
operation may be sent to the parent operation without being written to disk
Thus total number of block transfers for external sorting:br ( 2 logM–1(br / M) + 1)
Seeks: next slide
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
External Merge Sort (Cont.)
Cost of seeks During run generation: one seek to read each run and one seek to
write each run 2 br / M
During the merge phase Buffer size: bb (read/write bb blocks at a time)
Need 2 br / bb seeks for each merge pass except the final one which does not require a write
Total number of seeks: 2 br / M + br / bb (2 logM–1(br / M) -1)
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Join Operation
Several different algorithms to implement joins Nested-loop join Block nested-loop join Indexed nested-loop join Merge-join Hash-join
Choice based on cost estimate Examples use the following information
Number of records of customer: 10,000 depositor: 5000 Number of blocks of customer: 400 depositor: 100
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Nested-Loop Join
To compute the theta join r sfor each tuple tr in r do begin
for each tuple ts in s do begintest pair (tr,ts) to see if they satisfy the join condition if they do, add tr • ts to the result.
endend
r is called the outer relation and s the inner relation of the join. Requires no indices and can be used with any kind of join
condition. Expensive since it examines every pair of tuples in the two
relations.
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Nested-Loop Join (Cont.) In the worst case, if there is enough memory only to hold one block of
each relation, the estimated cost is nr bs + br block transfers, plus nr + br seeks
If the smaller relation fits entirely in memory, use that as the inner relation. Reduces cost to br + bs block transfers and 2 seeks
Assuming worst case memory availability cost estimate is with depositor as outer relation:
5000 400 + 100 = 2,000,100 block transfers, 5000 + 100 = 5100 seeks
with customer as the outer relation 10000 100 + 400 = 1,000,400 block transfers and 10,400 seeks
If smaller relation (depositor) fits entirely in memory, the cost estimate will be 500 block transfers.
Block nested-loops algorithm (next slide) is preferable.
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Block Nested-Loop Join
Variant of nested-loop join in which every block of inner relation is paired with every block of outer relation.
for each block Br of r do beginfor each block Bs of s do begin
for each tuple tr in Br do beginfor each tuple ts in Bs do begin
Check if (tr,ts) satisfy the join condition
if they do, add tr • ts to the result.end
endend
end
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Block Nested-Loop Join (Cont.) Worst case estimate: br bs + br block transfers + 2 * br seeks
Each block in the inner relation s is read once for each block in the outer relation (instead of once for each tuple in the outer relation
Best case: br + bs block transfers + 2 seeks. Improvements to nested loop and block nested loop
algorithms: In block nested-loop, use M — 2 disk blocks as blocking unit for
outer relations, where M = memory size in blocks; use remaining two blocks to buffer inner relation and output Cost = br / (M-2) bs + br block transfers +
2 br / (M-2) seeks If equi-join attribute forms a key or inner relation, stop inner loop
on first match Scan inner loop forward and backward alternately, to make use of
the blocks remaining in buffer (with LRU replacement) Use index on inner relation if available (next slide)
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Indexed Nested-Loop Join Index lookups can replace file scans if
join is an equi-join or natural join and an index is available on the inner relation’s join attribute
Can construct an index just to compute a join.
For each tuple tr in the outer relation r, use the index to look up tuples in s that satisfy the join condition with tuple tr.
Worst case: buffer has space for only one page of r, and, for each tuple in r, we perform an index lookup on s.
Cost of the join: br (tT + tS) + nr c Where c is the cost of traversing index and fetching all matching s
tuples for one tuple or r c can be estimated as cost of a single selection on s using the join
condition. If indices are available on join attributes of both r and s,
use the relation with fewer tuples as the outer relation.
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Example of Nested-Loop Join Costs
Compute depositor customer, with depositor as the outer relation. Let customer have a primary B+-tree index on the join attribute
customer-name, which contains 20 entries in each index node. Since customer has 10,000 tuples, the height of the tree is 4, and
one more access is needed to find the actual data depositor has 5000 tuples Cost of block nested loops join
400*100 + 100 = 40,100 block transfers + 2 * 100 = 200 seeks assuming worst case memory may be significantly less with more memory
Cost of indexed nested loops join 100 + 5000 * 5 = 25,100 block transfers and seeks. CPU cost likely to be less than that for block nested loops join
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Merge-Join1. Sort both relations on their join attribute (if not already sorted on the
join attributes).2. Merge the sorted relations to join them
1. Join step is similar to the merge stage of the sort-merge algorithm. 2. Main difference is handling of duplicate values in join attribute — every
pair with same value on join attribute must be matched3. Detailed algorithm in book
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Merge-Join (Cont.) Can be used only for equi-joins and natural joins Each block needs to be read only once (assuming all tuples for
any given value of the join attributes fit in memory Thus the cost of merge join is:
br + bs block transfers + br / bb + bs / bb seeks + the cost of sorting if relations are unsorted.
hybrid merge-join: If one relation is sorted, and the other has a secondary B+-tree index on the join attribute Merge the sorted relation with the leaf entries of the B+-tree . Sort the result on the addresses of the unsorted relation’s tuples Scan the unsorted relation in physical address order and merge with
previous result, to replace addresses by the actual tuplesSequential scan more efficient than random lookup
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Hash-Join
Applicable for equi-joins and natural joins. A hash function h is used to partition tuples of both relations h maps JoinAttrs values to {0, 1, ..., n}, where JoinAttrs denotes
the common attributes of r and s used in the natural join. r0, r1, . . ., rn denote partitions of r tuples
Each tuple tr r is put in partition ri where i = h(tr [JoinAttrs]).
r0,, r1. . ., rn denotes partitions of s tuplesEach tuple ts s is put in partition si, where i = h(ts [JoinAttrs]).
Note: In book, ri is denoted as Hri, si is denoted as Hsi and n is denoted as nh.
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Hash-Join (Cont.)
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Hash-Join (Cont.)
r tuples in ri need only to be compared with s tuples in si
Need not be compared with s tuples in any other partition, since: an r tuple and an s tuple that satisfy the join condition will have
the same value for the join attributes. If that value is hashed to some value i, the r tuple has to be in ri
and the s tuple in si.
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Hash-Join Algorithm
1. Partition the relation s using hashing function h. When partitioning a relation, one block of memory is reserved as the output buffer for each partition.
2. Partition r similarly.3. For each i:
(a)Load si into memory and build an in-memory hash index on it using the join attribute. This hash index uses a different hash function than the earlier one h.
(b)Read the tuples in ri from the disk one by one. For each tuple tr locate each matching tuple ts in si using the in-memory hash index. Output the concatenation of their attributes.
The hash-join of r and s is computed as follows.
Relation s is called the build input and r is called the probe input.
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Hash-Join algorithm (Cont.)
The value n and the hash function h is chosen such that each si should fit in memory. Typically n is chosen as bs/M * f where f is a “fudge factor”,
typically around 1.2 The probe relation partitions si need not fit in memory
Recursive partitioning required if number of partitions n is greater than number of pages M of memory. instead of partitioning n ways, use M – 1 partitions for s Further partition the M – 1 partitions using a different hash function Use same partitioning method on r Rarely required: e.g., recursive partitioning not needed for relations
of 1GB or less with memory size of 2MB, with block size of 4KB.
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Handling of Overflows Partitioning is said to be skewed if some partitions have
significantly more tuples than some others Hash-table overflow occurs in partition si if si does not fit in
memory. Reasons could be Many tuples in s with same value for join attributes Bad hash function
Overflow resolution can be done in build phase Partition si is further partitioned using different hash function. Partition ri must be similarly partitioned.
Overflow avoidance performs partitioning carefully to avoid overflows during build phase E.g. partition build relation into many partitions, then combine them
Both approaches fail with large numbers of duplicates Fallback option: use block nested loops join on overflowed partitions
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Cost of Hash-Join If recursive partitioning is not required: cost of hash join is
3(br + bs) +4 nh block transfers +
2( br / bb + bs / bb) seeks If recursive partitioning required:
number of passes required for partitioning build relation s is logM–1(bs) – 1
best to choose the smaller relation as the build relation. Total cost estimate is:
2(br + bs logM–1(bs) – 1 + br + bs block transfers + 2(br / bb + bs / bb) logM–1(bs) – 1 seeks
If the entire build input can be kept in main memory no partitioning is required Cost estimate goes down to br + bs.
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Example of Cost of Hash-Join
Assume that memory size is 20 blocks bdepositor= 100 and bcustomer = 400. depositor is to be used as build input. Partition it into five partitions,
each of size 20 blocks. This partitioning can be done in one pass. Similarly, partition customer into five partitions,each of size 80.
This is also done in one pass. Therefore total cost, ignoring cost of writing partially filled blocks:
3(100 + 400) = 1500 block transfers +2( 100/3 + 400/3) = 336 seeks
customer depositor
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Hybrid Hash–Join Useful when memory sized are relatively large, and the build input
is bigger than memory. Main feature of hybrid hash join: Keep the first partition of the build relation in memory. E.g. With memory size of 25 blocks, depositor can be partitioned
into five partitions, each of size 20 blocks. Division of memory:
The first partition occupies 20 blocks of memory1 block is used for input, and 1 block each for buffering the other 4
partitions. customer is similarly partitioned into five partitions each of size 80
the first is used right away for probing, instead of being written out Cost of 3(80 + 320) + 20 +80 = 1300 block transfers for
hybrid hash join, instead of 1500 with plain hash-join. Hybrid hash-join most useful if M >>
sb
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Complex Joins Join with a conjunctive condition:
r 1 2... n s Either use nested loops/block nested loops, or Compute the result of one of the simpler joins r i s
final result comprises those tuples in the intermediate result that satisfy the remaining conditions
1 . . . i –1 i +1 . . . n
Join with a disjunctive condition
r 1 2 ... n s Either use nested loops/block nested loops, or Compute as the union of the records in individual joins r i s:
(r 1 s) (r 2 s) . . . (r n s)
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Other Operations Duplicate elimination can be implemented via hashing or
sorting. On sorting duplicates will come adjacent to each other, and all but
one set of duplicates can be deleted. Optimization: duplicates can be deleted during run generation as well
as at intermediate merge steps in external sort-merge. Hashing is similar – duplicates will come into the same bucket.
Projection: perform projection on each tuple followed by duplicate elimination.
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Other Operations : Aggregation
Aggregation can be implemented in a manner similar to duplicate elimination. Sorting or hashing can be used to bring tuples in the same group
together, and then the aggregate functions can be applied on each group.
Optimization: combine tuples in the same group during run generation and intermediate merges, by computing partial aggregate valuesFor count, min, max, sum: keep aggregate values on tuples found so far
in the group. When combining partial aggregate for count, add up the aggregates
For avg, keep sum and count, and divide sum by count at the end
Computing & Information SciencesKansas State UniversityMonday, 03 Nov 2008CIS 560: Database System Concepts
Other Operations : Set Operations Set operations (, and ): can either use variant of merge-join
after sorting, or variant of hash-join. E.g., Set operations using hashing:
1. Partition both relations using the same hash function2. Process each partition i as follows.
1. Using a different hashing function, build an in-memory hash index on ri.2. Process si as follows
r s: 1. Add tuples in si to the hash index if they are not already in it. 2. At end of si add the tuples in the hash index to the result.
r s: 1. output tuples in si to the result if they are already there in the hash index
r – s: 1. for each tuple in si, if it is there in the hash index, delete it from the index. 2. At end of si add remaining tuples in the hash index to the result.